In Photo library i got duplicates pictures but the duplicate options is not appearing

According to Apple, depending on "the size of your photo library, the process could happen quickly or take up to a few days to complete". In reality, the process could take longer, such as a couple of weeks, if you have a large library. You will have to wait. You may see this message in the Duplicates album.

Photos will finish scanning for duplicates when you're not using the app and your Mac is connected to power.

If you are looking for a quick way to get rid of duplicates in Photos, you can try duplicate file finder software like Cisdem Duplicate Finder. It's designed to support working with the Photos app and also folders. Note that it's a paid app. It allows you to find and view duplicates though. If you prefer to using the built-in duplicate detection in Photos, you can just wait.

Have you checked to see if these "duplicates" are, in fact, duplicates? That is, do they have the same filename? Do they have the same date? Are they the same file size? Photos does pretty well with pictures if there are slight differences, but it may miss things that it thinks are different on purpose.

They sure look the same-- same resolution, same filename, same time. The third one is highly compressed, so the picture will look fuzzier when you zoom in. Throw it away!

If I were you, I'd not worry about it for awhile. A new macOS, Sequoia, will release in September, and upgrading should cause re-scans of the Photos Library. It may all fix itself then.

A big advantage in merging duplicates detected by Photos is that when you merge duplicates, their attributes are combined, and the result goes in every album either picture was in. I have many pictures imported from old backups that duplicate some pictures, but they are in different albums. Merging will reduce that to one picture that's listed in all the original albums. This is very cool!

Good Luck!